Explicit Price Discrimination

Transcription

1 Chapter 10 Explicit Price Discrimination 10.1 Motivation and objectives Broadly Figure 10.1 $ 30 Consumer surplus Deadweight loss Profit mc(q) 5 Cost d(p ) Q Figure 10.1 shows our familiar illustration of the deadweight loss and of the distribution of surplus for a firm with market power. The firm s manager is happy to see the large region labeled profit, but she feels disappointed for two reasons. First, the customers are getting away with some surplus. Second, some potential gains from trade (the deadweight loss) are not realized and hence go to no one. Ideally, she would like to generate all possible gains from trade and extract these gains for the firm. Her problem is not a lack of bargaining power. Her firm can make a take-it-or-leave-it price offer that allows for no haggling. Yet changing the price trades off consumer surplus for deadweight loss and so cannot eliminate both of them. Chapters 10, 11, and 11B examine more sophisticated pricing strategies that increase profits by expanding gains from trade and reducing consumer surplus. Firms, Prices, and Markets August 2012 Timothy Van Zandt

2 174 Explicit Price Discrimination Chapter 10 More specifically The pricing we studied in the previous two chapters is so standard that it needed neither a special term nor a definition until now, as we move toward more sophisticated strategies. Henceforth, we refer to the pricing from those chapters as uniform pricing. The other pricing strategies that we consider in Chapters 10, 11, and 11B are broadly classified as price discrimination. For now, it would be premature to define the distinction between uniform pricing and price discrimination. We will do so at the end of Chapter 11B, when we can reflect back on the various pricing strategies. A property of uniform pricing that we move away from in the current chapter is equal treatment of customers that the firm offers all customers the same options for trade. Customers have heterogeneous characteristics, so a firm can raise its profit by charging a higher price to customers with higher valuations. Such differential treatment is called explicit price discrimination. This chapter studies a common and simple form of explicit price discrimination in which the firm charges different prices to two or more market segments: pharmaceutical companies charge different prices in different countries; movie theaters and ski resorts have discounts for senior citizens; utility companies have different rates for residential and business customers; some countries that rely on income from tourism enforce a system of differential pricing for foreign visitors and (less wealthy) local residents. What differences between the demand curves of two market segments leads the firm to charge a higher price to one segment than to the other? This is similar to the question we asked (and answered) in Chapter 9 except that, in Chapter 9, the two demand curves were before and after a shift in demand. The bottom-line conclusion remains nearly the same: Charge a higher price to the market segment with less elastic demand. The conclusion is even simpler here because there is no mention of volume and of the shape of the marginal cost curve. (In particular, there is no volume effect.) The marginal cost of selling one more unit is the same for both market segments because they are served by the same firm and from the same production process Requirements for explicit price discrimination Examples A market segment means a subgroup of customers. It is sometimes the case that a firm can charge a different price to different market segments. If the demand curves in the different segments have sufficiently different properties, then such explicit price discrimination can

3 Section 2 Requirements for explicit price discrimination 175 raise the firm s profit. Here are some examples. 1. A firm can offer student or senior-citizen discounts, enforced by requiring a student ID or proof of age. 2. A utility company may charge different rates to business and residential customers. 3. A pharmaceutical company can charge different prices in different countries for prescription medicine. 4. A pharmaceutical company can charge different prices for the same medicine depending on what it is prescribed for. 5. A software company can give an academic discount to people who have an academic affiliation. Observability and no-resale In each of the five examples, customers in a market segment that is charged a higher price may try to circumvent the price discrimination by either: pretending they belong to the other segment, which is called masquerading ; or buying the product through customers in the other segment, which is called arbitrage. Explicit price discrimination is effective only if such masquerading and arbitrage are difficult or at least inconvenient. The following would be examples of masquerading: a non-student uses a fake student ID in order to receive the student discount at a theater; a person running a business from his own home does not disclose this fact in order to obtain residential rates from a utility company; a patient with one ailment buys a medicine using a prescription for a different ailment. Masquerading occurs when the characteristic used for explicit price discrimination is not observable. Therefore, we refer to the lack of masquerading as the observability condition. The following would be examples of arbitrage: a person buys prescription medicine in India and resells it in the United States; a professor buys a software package for a friend in order to get the academic discount. Arbitrage occurs when resale between customer segments is possible. Therefore, we refer to the lack of arbitrage as the no-resale condition. Observability and no-resale are satisfied in the five examples of explicit price discrimination that we gave ealier. (Remember that this means merely that masquerading and arbitrage are at least inconvenient not that they are impossible.) However, these conditions are stringents and being able to explicitly segment a market is the exception rather than the rule. For example, because the income level of concert goers is not observable, it is not possible to charge wealthier customers higher prices for the same tickets. Resale makes it ineffective for a book retailer to charge different prices to men and to women; it would be very easy for (say) a man to get a woman to buy a book for him.

4 176 Explicit Price Discrimination Chapter 10 Explicit price discrimination is nearly impossible if a product is sold through a retailer and the producing firm never has contact with the customer. A retailer of art supplies might offer a discount to local art students thus having different mark-ups for different customers, which is to say different prices for its retailing services. However, the manufacturer of the art supplies would find it difficult to offer different wholesale prices that depend on the final customer who buys the product. In order to avoid masquerading, Apple offers an academic discount only at its own stores and through a limited number of authorized retailers, which must provide documentation to Apple each time they sell a computer with the discount. In order to avoid arbitrage, Apple limits the number of computers an individual can purchase with the discount. Avoiding masquerading and arbitrage may be possible yet require costly systems to track customers and products. Furthermore, merely charging different prices carries a complexity cost. The firm must weigh these transaction costs against the benefits of explicitly segmenting the market. There is a technology-based arms race between firms and customers that is constantly shifting the practicality of explicit price discrimination. On the one hand, information technology and internet-based transactions makes it easier to track customer characteristics and tailor offers to these characteristics. For example, Amazon has (controversially) used customers browsing and purchasing histories to adjust the prices that it charges different customers for the same book. On the other hand, this same technology makes trade more anonymous (facilitating masquerading) and makes it easier for customers to arbitrage price differences (for example, it has become easier to purchase prescription medicine from a foreign country by internet even though national laws restrict such trade). Exercise Explicit price discrimination tends to be more common in the sale of services (e.g., discrimination by income for universities and by age for air transportation services) than in the sale of manufactured goods. Why do you think this is so? A false example If you had to give another example of explicit price discrimination, you might mention business and leisure travelers who pay different prices for air travel. However, this would be wrong. The defining characteristic of explicit price discrimination is that customers have different trading opportunities. For example, a 40-year-old cannot get the children s discount at an amusement park. Is this true of the airlines pricing example? A business traveler and leisure traveler are sitting side by side in coach class on their way from Amsterdam to Barcelona. They converse and reveal that the business traveler paid 700 for her ticket whereas the leisure traveler paid 250 for his. Could the business traveler have bought the same ticket as the leisure traveler? Certainly. The leisure traveler purchased his ticket in advance, took a Saturday-night stay, and accepted penalties and non-

5 Section 3 Different prices for different segments 177 refundability in case of changes. The business traveler could have done the same but chose not to. Airlines cannot explicitly segment the market owing to masquerading: they cannot tell whether a customer is a business or leisure traveler. A business traveler does not have a B branded on her forehead, and there is no leisure-traveler s ID card that the airlines could demand before giving a leisure-traveler s discount. However, it is clear that airlines complex pricing of restricted and non-restricted tickets is closely related to explicit price discrimination. It is an example of implicit price discrimination, which is a way of indirectly and imperfectly pursuing the goals of explicit price discrimination when the latter is not possible. We will study this in Chapter 11. For now, as you read through the current chapter, it is still useful to ask yourself what airlines would do if they could explicitly segment the market. That is the first step toward understanding how they should handle implicit price discrimination Different prices for different segments As we have noted, the observability and no-resale conditions need only be approximately satisfied in order for a firm to explicitly segment a market. To simplify our model, we assume that the two conditions are perfectly satisfied and we ignore any transaction costs. Cost-based price differences that we do not study A firm may charge a higher price to one segment than another simply because it is more costly to serve customers in the first segment (as a result, e.g., of transportation costs). More commonly, such cost-based price differences are entangled with (but do not invalidate) the demand-based price differences that we study. Sometimes the two effects are difficult to untangle empirically. Does a laundry service charge more for a woman s blouse than for a man s shirt because the former are, on average, more difficult to iron? Or is it because of differences in the elasticity of demand for the market segments? Probably both factors are present. On the other hand, if a Japanese car manufacturer charges a lower price in the United States than in Japan for a car produced in Japan in spite of the transportation cost then differences in demand are driving the price difference. At an analytic level we can untangle the two effects by studying one effect at a time, just as we untangled the volume and price-sensitivity effects in Chapter 9. In this chapter, we devote all our time to the more-interesting demand-based effects. We neutralize the cost-based effects by assuming that the goods or services sold to the two segments are identical hence have the same production cost and that there are no transportation costs.

6 178 Explicit Price Discrimination Chapter 10 Bottom line There is no point in explicitly segmenting your market unless the demand curves of the segments are sufficiently different. What differences should there be? When we lack the data needed to calculate the profit-maximizing prices of the two segments, can we still use qualitative information about the segments to determine which segment should be charged a higher price? The bottom line is that the price-sensitivity effect studied in Chapter 9 arises here as well, but is even more robust because there is no volume effect: Your firm should charge a higher price to the segment with less elastic demand. Marginal conditions for revenue maximization This conclusion again comes from studying marginal conditions. Suppose you have two market segments, which we label 1 and 2. Once again, though we want to understand price, we attack the problem by framing it in terms of quantities: your must choose the amounts Q 1 and Q 2 to sell to the two segments. Recall that we assume the output comes from a common production process without transportation costs. Then total cost is a function of the total amount supplied to all segments, not of how it is divided among the segments. The marginal cost of producing another unit is the same no matter which segment it goes to. Let s think about the decomposition of your problem between production and marketing. Production. On the production side, we simply have a cost curve c(q) measuring cost as a function of total output Q = Q 1 + Q 2 ; our production managers need not concern themselves with price discrimination. Marketing. It is the task of the market managers to divide the output among the market segments in order to maximize revenue. Let r 1 (Q 1 ) and r 2 (Q 2 ) be the revenue from the two segments. Given total output Q, the marketing department s problem is to choose Q 1 and Q 2 (such that Q 1 +Q 2 = Q) in order to maximize total revenue r 1 (Q 1 )+r 2 (Q 2 ). The total amount of revenue that can be obtained depends on Q; denote this by r(q). Strategic planning. The central strategy group chooses Q to maximize r(q) c(q). If the firm is to maximize profit, each group must do its job right. For the marketing department, this means that they divide the output among the segments to obtain the highest possible revenue from what has been produced. The marginal condition is MR 1 = MR 2 ; otherwise, revenue can be increased by shifting output from the segment with low marginal revenue to the segment with high marginal revenue. For example, if MR 1 > MR 2,then shifting one unit of output from segment 2 to segment 1 increases total revenue by MR 1 MR 2. As in Chapter 9, the equality MR 1 = MR 2 allows us to conclude that the price is higher

7 Section 3 Different prices for different segments 179 for the less elastic demand curve. Recall the formula ( MR = P 1 1 ). E Suppose demand is more elastic in segment 1 than in segment 2. As a benchmark, let output be divided so that the same price P holds in both market segments. Then E 1 >E 2 at the common price and ) ) MR 1 = P (1 1E1 >P (1 1E2 = MR 2. Because MR 1 > MR 2, revenue can be increased by shifting output from segment 2 to segment 1, causing the price to fall in segment 1 and to rise in segment 2. Therefore, the optimal division of output is such that the price in segment 1 is lower than in segment 2. (This argument assumes that marginal conditions are sufficient, but there is an alternative proof of the same result without such an assumption.) For example, suppose that d 1 (P ) = 20 P and d 2 (P ) = 60 2P. (10.1) The choke prices are P 1 = 20 and P 2 = 30, so the demand in segment 1 is more elastic demand than that in segment 2. Therefore, you should charge less to segment 1 than to segment 2. Determining the optimal level of production This price comparison is the main point of this section. However, let s complete the analysis by including the strategic planning problem in order to see how quantities and prices are calculated. There are three cases. Constant marginal cost. Each market segment represents an independent uniform pricing problem. You solve the two separate equations: mr 1 (Q 1 ) = MC, and mr 2 (Q 2 ) = MC. For example, suppose you have constant marginal cost of 10 and that the demand curves are those in equation (10.1). Using the midpoint pricing rule, your optimal prices are P 1 = ( P 1 + MC)/2 = ( )/2 = 15,and P 2 = ( P 1 + MC)/2 = ( )/2 = 20. Observe that P 1 <P 2 as predicted. Increasing marginal cost. If marginal cost is not constant, then pricing across different segments is interrelated because the marginal cost is a function of the total amount pro-

8 180 Explicit Price Discrimination Chapter 10 duced. The optimal quantities Q 1 and Q 2 should solve the system of equations mr 1 (Q 1 ) = mc(q 1 + Q 2 ), mr 2 (Q 2 ) = mc(q 1 + Q 2 ). For the demand curves in equation (10.1), mr 1 (Q 1 ) = 20 2Q 1 and mr 2 (Q 2 ) = 30 Q 2. Suppose that c(q) = Q + Q 2 /4 and hence mc(q) = 1 + Q/2. The equations are then 20 2Q 1 = 1 + (Q 1 + Q 2 )/2, 30 Q 2 = 1 + (Q 1 + Q 2 )/2. One can verify that the solution is Q 1 = 4 and Q 2 = 18, which corresponds to prices P 1 = 16 and P 2 = 21. Again,P 1 <P 2 as predicted. Fixed capacity. Suppose you have a fixed capacity Q. Then you split this capacity to equate marginal revenue in the segments, solving mr 1 (Q 1 ) = mr 2 (Q 2 ), Q 1 + Q 2 = Q. Sticking to the same demand curves and assuming Q = 34, these equations are 20 2Q 1 = 30 Q 2, Q 1 + Q 2 = 34. One can verify that the solution is Q 1 = 8 and Q 2 = 26, which correspond to prices P 1 = 12 and P 2 = 17. Once again, P 1 <P Wrap-up By charging different prices to different market segments assuming that the firm can observe some characteristic that differentiates demand the firm can increase total surplus and appropriate more of this surplus. The main conclusion is that the firm charges a higher price in the market segment whose demand is less elastic.